A MIMO system is one in which a transmitter employs multiple antennae for transmitting data to a receiver. The data may consist of multiple data streams. The signal transmitted at each transmitter antenna is a linear combination of data streams. The receiver that is intended to receive the data streams and recover the data may have more than one reception antenna such that there is receive diversity as well as transmit diversity. Generally speaking, a system can still be described as a special case of MIMO [also known as MISO] when there is in practice one reception antenna working with signals from multiple transmitter antennae.
MIMO is used in the IEEE 802.11 standards to enhance the data rate provided by the physical layer in a transmission link between a transmitter and a receiver. Beam-forming feedback is a critical step to enable the transmitter to optimise MIMO transmission to maximise the data rate of the transmission link to the receiver. In explicit beam-forming feedback, the receiver informs the transmitter about the preferred beam-forming matrix. The beam-forming matrix is sometimes known as the spatial mapping matrix. The beam-forming matrix has a number of columns equal to the number Ns of spatial streams in the MIMO scheme and a number Nt of rows equal to the number of transmit antennae in the MIMO scheme. More precisely, there is a row for each transmitter antenna and a column for each spatial stream. The columns are often referred to as beam-forming vectors since each column provides the set of complex-valued, beam-forming weights that are to be applied to the transmitter antennae for the spatial stream to which the column in question corresponds.
In MIMO schemes, consideration must be given to how to quantise the beam-forming matrix and represent the beam-forming matrix with a limited number of bits.
A natural solution to quantise the beam-forming matrix is to use Nb bits to quantise the real part and another Nb bits to quantise the imaginary part of each of its elements. Thus, for a beam-forming matrix with dimension Nt×Ns, the beam-forming feedback requires 2×Nb×Nt×Ns bits per matrix. This type of direct quantisation will be referred to hereinafter as “Cartesian quantisation”.